Find the Exact Value tan((11pi)/3)

Problem

tan((11*π)/3)

Solution

1. Find the coterminal angle within the standard interval [0,2*π) by subtracting 2*π from the given angle.

(11*π)/3−2*π=(11*π)/3−(6*π)/3

(11*π)/3−(6*π)/3=(5*π)/3

2. Identify the quadrant for the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle lies in Quadrant IV.

3. Determine the reference angle θ′ for an angle in Quadrant IV using the formula θ′=2*π−θ

θ′=2*π−(5*π)/3

θ′=π/3

4. Apply the tangent value for the reference angle π/3

tan(π/3)=√(,3)

5. Determine the sign of the tangent function in Quadrant IV. Since tangent is negative in Quadrant IV, the result must be negative.

tan((5*π)/3)=−√(,3)

Final Answer

tan((11*π)/3)=−√(,3)

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